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Simplifying 2x2 + -21x + -60 = 0 Reorder the terms: -60 + -21x + 2x2 = 0 Solving -60 + -21x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -30 + -10.5x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -10.5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -10.5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -10.5x + x2 = 0 + 30 -10.5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -10.5x + x2 = 30 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = 30 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = 30 + 27.5625 Combine like terms: 30 + 27.5625 = 57.5625 27.5625 + -10.5x + x2 = 57.5625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 57.5625 Calculate the square root of the right side: 7.586995453 Break this problem into two subproblems by setting (x + -5.25) equal to 7.586995453 and -7.586995453.Subproblem 1
x + -5.25 = 7.586995453 Simplifying x + -5.25 = 7.586995453 Reorder the terms: -5.25 + x = 7.586995453 Solving -5.25 + x = 7.586995453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 7.586995453 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 7.586995453 + 5.25 x = 7.586995453 + 5.25 Combine like terms: 7.586995453 + 5.25 = 12.836995453 x = 12.836995453 Simplifying x = 12.836995453Subproblem 2
x + -5.25 = -7.586995453 Simplifying x + -5.25 = -7.586995453 Reorder the terms: -5.25 + x = -7.586995453 Solving -5.25 + x = -7.586995453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -7.586995453 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -7.586995453 + 5.25 x = -7.586995453 + 5.25 Combine like terms: -7.586995453 + 5.25 = -2.336995453 x = -2.336995453 Simplifying x = -2.336995453Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.836995453, -2.336995453}
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